A 2-tree is recursively defined as follows: K_2 is a 2-tree and any 2-tree on n+1 vertices is obtained by joining a vertex to a 2-clique in a 2-tree on n vertices. Care is needed with the term 2-tree (and k-tree in general) because it has at least two commonly used definitions.

A036361 gives the labeled version of this sequence, which has an easy formula analogous to Cayley's formula for the number of trees.

a(1)=a(2)=a(3)=1 because: K_2, K_3 are the only 2-trees on 2 and 3 nodes and on 4 nodes, there is a also unique example obtained by joining a triangle to K_3 along an edge (thus forming K_4\e). The two graphs on 5 nodes are obtained by joining a triangle to K_4\e, either along the shared edge or along one of the non-shared edges.